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lazy-ski.ss
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lazy-ski.ss
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(load "pmatch.scm")
(define occur-free?
(lambda (y exp)
(pmatch exp
[,x (guard (symbol? x)) (eq? y x)]
[(lambda (,x) ,e) (and (not (eq? y x)) (occur-free? y e))]
[(,rator ,rand) (or (occur-free? y rator) (occur-free? y rand))])))
(define value?
(lambda (exp)
(pmatch exp
[,x (guard (symbol? x)) #t]
[(lambda (,x) ,e) #t]
[(,rator ,rand) #f])))
(define app? (lambda (x) (not (value? x))))
(define term-length
(lambda (exp)
(pmatch exp
[,x (guard (symbol? x)) 0]
[(lambda (,x) ,e) (+ 1 (term-length e))]
[(,rator ,rand) (+ 1 (term-length rator) (term-length rand))])))
; call-by-name compiler to S, K, I
(define compile
(lambda (exp)
(pmatch exp
[,x (guard (symbol? x)) x]
[(,M ,N) `(,(compile M) ,(compile N))]
[(lambda (,x) (,M ,y))
(guard (eq? x y) (not (occur-free? x M))) (compile M)]
[(lambda (,x) ,y) (guard (eq? x y)) `I]
[(lambda (,x) (,M ,N)) (guard (or (occur-free? x M) (occur-free? x N)))
`((S ,(compile `(lambda (,x) ,M))) ,(compile `(lambda (,x) ,N)))]
[(lambda (,x) ,M) (guard (not (occur-free? x M))) `(K ,(compile M))]
[(lambda (,x) ,M) (guard (occur-free? x M))
(compile `(lambda (,x) ,(compile M)))])))
; call-by-name compiler to S, K, I, B, C
(define compile-bc
(lambda (exp)
(pmatch exp
[,x (guard (symbol? x)) x]
[(,M ,N) `(,(compile-bc M) ,(compile-bc N))]
[(lambda (,x) ,y) (guard (eq? x y)) `I]
[(lambda (,x) (,M ,y))
(guard (eq? x y) (not (occur-free? x M))) (compile-bc M)]
[(lambda (,x) (,M ,N)) (guard (and (not (occur-free? x M)) (occur-free? x N)))
`((B ,(compile-bc M)) ,(compile-bc `(lambda (,x) ,N)))]
[(lambda (,x) (,M ,N)) (guard (and (occur-free? x M) (not (occur-free? x N))))
`((C ,(compile-bc `(lambda (,x) ,M))) ,(compile-bc N))]
[(lambda (,x) (,M ,N)) (guard (or (occur-free? x M) (occur-free? x N)))
`((S ,(compile-bc `(lambda (,x) ,M))) ,(compile-bc `(lambda (,x) ,N)))]
[(lambda (,x) ,M) (guard (not (occur-free? x M))) `(K ,(compile-bc M))]
[(lambda (,x) ,M) (guard (occur-free? x M))
(compile-bc `(lambda (,x) ,(compile-bc M)))])))
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; ski->lanbda converter
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; create gensyms
(define fv
(let ((n -1))
(lambda (x)
(set! n (+ 1 n))
(string->symbol
(string-append (symbol->string x) "." (number->string n))))))
;; substitution with free variable capturing avoiding
(define subst
(lambda (x y exp)
(pmatch exp
[,u (guard (symbol? u)) (if (eq? u x) y u)]
[(lambda (,u) ,e)
(cond
[(eq? u x) exp]
[(occur-free? u y) ; possible capture, switch names
(let* ([u* (fv u)]
[e* (subst u u* e)])
`(lambda (,u*) ,(subst x y e*)))]
[else
`(lambda (,u) ,(subst x y e))])]
[(,e1 ,e2) `(,(subst x y e1) ,(subst x y e2))]
[,exp exp])))
; combinator definitions
(define com-table
'((S . (lambda (f) (lambda (g) (lambda (x) ((f x) (g x))))))
(K . (lambda (x) (lambda (y) x)))
(I . (lambda (x) x))
(B . (lambda (f) (lambda (g) (lambda (x) (f (g x))))))
(C . (lambda (a) (lambda (b) (lambda (c) ((a c) b)))))))
; substitute combinator with their lambda term definitions
(define sub-com
(lambda (exp defs)
(cond
[(null? defs) exp]
[else (sub-com (subst (caar defs) (cdar defs) exp) (cdr defs))])))
(define ski->lambda
(lambda (exp)
(sub-com exp com-table)))
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; tests
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(define to-number `(lambda (n) ((n (lambda (x) (,add1 x))) 0)))
(interp `(,to-number ,(ski->lambda (compile-bc `(,!-n ,lfive)))))
; => 120
(term-length `(,! ,lfive))
; => 93
(term-length (compile `(,! ,lfive)))
; => 144
(term-length (compile-bc `(,! ,lfive)))
; => 73